
where effective potential \(V_{\rm eff}(\varphi ,0)\)  is given in Eq. (REF ), which contains one-loop level quantum correctionsOne-loop corrections to the \(hhh\)  coupling in extended Higgs models is discussed in Ref. [1]}, [2]}, [3]}, [4]}, [5]}.
Typically, the two-loop effects give positive contributions to the \(hhh\)  coupling, which are about 20\(\%\)  of those at one-loop [6]}, [7]}, [8]}..
Therefore, the strongly first-order EWPT can be tested by precisely measuring the \(hhh\)  coupling at future collider experiments [9]}.
At the HL-LHC, the \(hhh\)  coupling can be measured at 50 \(\%\)  accuracy (at the 68\(\%\)  confidence level) [10]}, while at the future lepton collider such as the ILC energy upgraded version with the energy 500 GeV and 1 TeV, the \(hhh\)  coupling is expected to be measured by 27\(\%\)  and 10\(\%\)  accuracies (at the 68\(\%\)  confidence level), respectively [11]}.
